Answer:
Uwu
Step-by-step explanation:
Answer:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
Step-by-step explanation:
y" + y' + y = 1
This is a second order nonhomogenous differential equation with constant coefficients.
First, find the roots of the complementary solution.
y" + y' + y = 0
r² + r + 1 = 0
r = [ -1 ± √(1² − 4(1)(1)) ] / 2(1)
r = [ -1 ± √(1 − 4) ] / 2
r = -1/2 ± i√3/2
These roots are complex, so the complementary solution is:
y = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t)
Next, assume the particular solution has the form of the right hand side of the differential equation. In this case, a constant.
y = c
Plug this into the differential equation and use undetermined coefficients to solve:
y" + y' + y = 1
0 + 0 + c = 1
c = 1
So the total solution is:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
To solve for c₁ and c₂, you need to be given initial conditions.
Answer:
The value is a statistic, since it is from a sample.
Step-by-step explanation:
If the value is from a population, it is a parameter.
Otherwise, if the value is from a sample, it is a statistic.
In this question:
In a random sample of U.S. households, it was found that 72% have high-speed Internet.
The value is from a sample, so it is a statistic.
To solve this problem you must apply the proccedure shown below:
1. You must apply the following formula:
Where 
is the future value, 
is the present value, 
is the interest rate and 
is the time in years.
2. You have that the bank will double your money in 
years. Therefore:
3. Substitute values into the formula and solve for , as following:
4. By applying natural logarithm, you have:
%
The answer is: 
%
Step-by-step explanation:
the slope is always the ratio "y coordinate charge / x coordinate change" when going from one point on the line to another.
so, when going from (-2, 1) to (4, -3)
x changes by +6 (from -2 to 4).
y changes by -4 (from 1 to -3).
therefore, the slope is
-4/+6 = -4/6 = -2/3
